Problem P. 5261. (November 2020)
P. 5261. The winner of stage 7 of the 2017 Tour de France was judged by photo finish. According to the photo finish Michael Kittel was only 6 millimetres ahead of Edvald Boason Hagen, the second, and their time difference was only 3 ten-thousands of a second.
\(\displaystyle a)\) At what speed did the cyclists travel at the finish?
\(\displaystyle b)\) According to the official results the first three riders covered the 213.5 km distance during the same time of 5 hours 3 minutes and 18 seconds. What was the average speed of the riders for the whole distance?
\(\displaystyle c)\) What may be the reason that the time of the first three riders was recorded to be the same?
(3 pont)
Deadline expired on December 15, 2020.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás. \(\displaystyle a)\) A célba befutó első két versenyző sebessége
\(\displaystyle v_\text{cél}=\frac{6~\rm mm}{3\cdot 10^{-4}~\rm s}=20~\frac{\rm m}{\rm s}=72~\frac{\rm km}{\rm h}.\)
\(\displaystyle b)\) A megadott idő 5,055 órának felel meg, így az átlagsebesség
\(\displaystyle v_\text{átlag}=\frac{213{,}5~\rm km}{5{,}055 ~\rm h}=42{,}24~\frac{\rm km}{\rm h}\approx 42~\frac{\rm km}{\rm h}.\)
\(\displaystyle c)\) A célba érkezésnél az időkülönbségeket ezredmásodperces és milliméteres pontossággal tudják mérni, de a teljes táv megtételének idejét ennél sokkal nagyobb pontatlansággal ismerjük csak. Emiatt nincs értelme a teljes időt másodpercnél pontosabban megadni.
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Problems in Physics of KöMaL, November 2020